Eric Riemer Hare
Eric Hare, Heike Hofmann, Alicia Carriquiry
Iowa State University
April 14th, 2017
2009 NAS report: “much forensic evidence – including, for example, bite marks and firearm and toolmark identification is introduced in criminal trials without any meaningful scientific validation, determination of error rates, or reliability testing.” (National Research Council 2009)
From a September 2016 report by the Presidentâs Council of Advisors on Science and Technology (PCAST) titled Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods (Advisors on Science and Technology 2016):
A secondâand more importantâdirection is (as with latent print analysis)
to convert firearms analysis from a subjective method to an objective
method. This would involve developing and testing image-analysis
algorithms for comparing the similarity of tool marks on bullets. [...]
In a recent study, researchers used images from an earlier study to
develop a computer-assisted approach to match bullets that minimizes
human input [338].
338: Hare, E., Hofmann, H., and A. Carriquiry. âAutomatic matching of bullet lands.â Unpublished paper, available at: arxiv.org/pdf/1601.05788v2.pdf.
The key to this approach is the reference database…
plot3D.x3p.file(read_x3p("/Users/heike/papers/dissertations/eric-dissertation/images/Hamby (2009) Barrel/bullets/Br1 Bullet 1-5.x3p"),
plot.type = "surface")https://isu-csafe.stat.iastate.edu/shiny/bulletr/
We need to choose a location (height) of the bullet at which to extract a profile. To do so, we optimize the CCF (T. Vorburger et al. 2011):
Parameters: \(d = 25\mu m, d_0 = 25\mu m, c = 0.9\)
br111 <- get_crosscut("images/Br1 Bullet 1-5.x3p", x = 243.75)
qplot(y, value, data = br111) + theme_bw()The striations that identify a bullet to a gun barrel are located in the land impression areas (Xie et al. 2009).
Parameters: \(s = 35\mu m\)
br111.groove <- get_grooves(br111)
br111.groove$plotbr116 <- "/Users/heike/papers/dissertations/eric-dissertation/images/Hamby (2009) Barrel/bullets/Br1 Bullet 1-6.x3p"
result2 <- get_grooves(get_crosscut(br116))
result2$plotLocal weighted scatterplot smoothing (Cleveland 1979) - Fits a low-degree polynomial to a small subset of the data, weighting values near the point to be estimated more strongly.
br111.loess <- fit_loess(br111, br111.groove)
br111.loess$fittedDeviations from the loess fit should represent the imperfections (striations) on the bullet. Hence, we extract the residuals from the model.
br111.loess$residAs with detecting the shoulders, we can smooth the deviations and compute derivatives to identify peaks and valleys in the signature.
br111.peaks <- get_peaks(br111.loess$data)
br111.peaks$plotThe previous five steps are performed for each bullet land. But now we wish to extract features for cross comparisons of bullet lands.
Features are extracted from each land-to-land comparison:
To begin to tackle the degraded bullet problem, we need to standardize features by the length of the recovered land.
Matches = 27, Matches per mm = 14.72
By standardizing the features, we don’t penalize the degraded case as in the first revision of our algorithm:
Matches = 8, Matches per mm = 11.42
Our algorithm had trouble in scenarios where large deformations in the two aligned signatures yielded a high CCF, when in fact the two land were not matches.
We fit a new loess fit to the average of the two signatures, and subtract the resulting fit from the original signatures - This models the “roughness” of the bullet land while removing the “waviness”
CCF: 0.7724
Roughness Correlation: -0.0324
In the typical case of no major deformations, the roughness correlation remains similar to the CCF and the resulting profiles don’t change much:
CCF: 0.6891
Roughness Correlation: 0.7980
Simulation Study:
To come full circle, we will attempt to extract a 50% degraded signature from a Hamby bullet land with band tank rash in one half. (Barrel 9 Bullet 2 Land 4):
Extracting the ideal signature and then simulating a left-fixed 50% degradation scenario yields the following:
By far the biggest limitation of these algorithms thus far is the limited amount of available 3D scan data for bullets:
11 unique gun barrels is not yet enough to form a true reference distribution for known matches and non-matches…
…However, the structure of the database means that as soon as new data is available, the features and scores can be easily recomputed.
Some work has been done to optimize the parameter choices (smoothing factor, optimal cross-section, etc.) But there are number of parameters which were chosen without cross-validation:
Further, the parameters we did optimize were chosen to be globally optimal rather than for each individual land or cross-comparison of lands. This was done for computational efficiency.
Special thanks to Alan Zheng at the National Institute of Standards and Technology for maintaining the NIST Ballistics Toolmark Research Database and providing many useful suggestions for our algorithm.
Any Questions?
Advisors on Science, President’s Council of, and Technology. 2016. “Report on Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods.” https://www.whitehouse.gov/sites/default/files/microsites/ostp/PCAST/pcast_forensic_science_report_final.pdf.
Biasotti, Alfred A. 1959. “A Statistical Study of the Individual Characteristics of Fired Bullets.” Journal of Forensic Sciences 4 (1): 34–50.
Chu, Wei, Robert M Thompson, John Song, and Theodore V Vorburger. 2013. “Automatic identification of bullet signatures based on consecutive matching striae (CMS) criteria.” Forensic Science International 231 (1–3): 137–41.
Clarkson, James A, and C Raymond Adams. 1933. “On Definitions of Bounded Variation for Functions of Two Variables.” Transactions of the American Mathematical Society 35 (4). JSTOR: 824–54.
Cleveland, William S. 1979. “Robust Locally Weighted Regression and Smoothing Scatterplots.” Journal of the American Statistical Association 74 (368). Taylor & Francis, Ltd.: 829–36. http://www.jstor.org/stable/2286407.
Giannelli, Paul C. 2011. “Ballistics Evidence Under Fire.” Criminal Justice 25 (4): 50–51.
Hamby, James E., David J. Brundage, and James W. Thorpe. 2009. “The Identification of Bullets Fired from 10 Consecutively Rifled 9mm Ruger Pistol Barrels: A Research Project Involving 507 Participants from 20 Countries.” AFTE Journal 41 (2): 99–110.
Hofmann, Heike, and Eric Hare. 2016. Bulletr: Algorithms for Matching Bullet Lands.
National Research Council. 2009. Strengthening Forensic Science in the United States: A Path Forward. Washington, DC: The National Academies Press. doi:10.17226/12589.
Nichols, Ronald G. 2003. “Consecutive Matching Striations (CMS): Its Definition, Study and Application in the Discipline of Firearms and Tool Mark Identification.” AFTE Journal 35 (3): 298–306.
OpenFMC. 2014. X3pr: Read/Write Functionality for X3p Surface Metrology Format.
Vorburger, T.V., J.-F. Song, W. Chu, L. Ma, S.H. Bui, A. Zheng, and T.B. Renegar. 2011. “Applications of Cross-Correlation Functions.” Wear 271 (3–4): 529–33. doi:http://dx.doi.org/10.1016/j.wear.2010.03.030.
Xie, F., S. Xiao, L. Blunt, W. Zeng, and X. Jiang. 2009. “Automated Bullet-Identification System Based on Surface Topography Techniques.” Wear 266 (5–6): 518–22. doi:http://dx.doi.org/10.1016/j.wear.2008.04.081.